9514 1404 393
Answer:
 about 3,160,000,000
Step-by-step explanation:
"Increases at a rate proportional to population" means the growth is exponential. It can be modeled by the equation ...
 p = ab^t
We can find 'a' and 'b' using the given data points.
 100 = ab^(-4) . . . . . . . population 4 days ago
 100,000 = ab^(-2) . . . population 2 days ago
Dividing the second equation by the first, we find ...
 1000 = b^2
 b = 1000^(1/2)
Substituting for b in the first equation, we have ...
 100 = a(1000^(1/2))^(-4) = a(1000^-2)
 100,000,000 = a
Then the population model is ...
 p = 100,000,000×1000^(t/2)
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Tomorrow (t=1), the population will be ...
 p = 100,000,000 × 1000^(1/2) ≈ 31.6 × 100,000,000
 p ≈ 3,160,000,000 . . . . . bacteria by tomorrow
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Additional comment
We could write this as ...
 p = 10^(8+1.5t)
Then for t=1, this is p = 10^(8+1.5) = 10^0.5 × 10^9 = 3.16×10^9
